Precise description of one-shot learning
The model has learnt the "features" for the type of inputs, eg. faces. 
For the problem to be called one-shot, it needs to also correctly classify/compare any new samples. For example, in face recognition application, any new person's images should also result a positive for their own image and negative for any other seen or unseen image.

Since we are using euclidean distance of the final feature layer and not performing any final classification, we can say we are using the weights of a pretrained network and computing final value using that(distance), thus transfer learning. There is no backprop in this, but what you want to do with the embeddings, such as learning a threshold function can be considered learning.